Strapdown inertial navigation systems are frequently used in missiles and aircraft. Physically isolated and stabilized apparatus, such as a gimballed platform that is physically angularly-stabilized relative to the local vertical direction, require precise and mechanically complex angle positioning apparatus, and are being systematically replaced by systems of the strapdown type.
A state-of-the-art strapdown inertial navigation system has three rotation sensors or gyros and three accelerometers rigidly attached to a supporting vehicle. The rotation sensors are each positioned and oriented to sense angular displacement about one of three defined orthogonal axes attached to the vehicle body and known as the body coordinate system. The accelerometers are each positioned and oriented in a fixed direction relative to the vehicle, to sense velocity changes (incremental velocities) along different ones of the three defined orthogonal axes. In a strapdown system, the accelerometer axes are not angularly stabilized.
Because the accelerometers are constantly changing direction relative to gravity, navigation velocities cannot be computed by directly integrating the accelerometer signals. Instead, a stable computational frame or analytic navigation coordinate system is continually generated. The output signals from the rotation sensors are used by an attitude integration apparatus to calculate the directions of local vertical, together with two other axes orthogonal to the local vertical direction.
Sensed angle changes and accelerations (incremental velocities) are continually rotated through the calculated angles from the vehicle body axes to the calculated navigation axes. Angle signals from the rotation sensors are used to update the computer-stored angular position and incremental velocity data for both the angle sensors and accelerometers relative to the navigation coordinate system.
The rotation sensors and accelerometers have fixed relative directions in the body coordinate system. An angular transformation matrix of direction cosines is computed in an attitude integration apparatus. The accelerometer signals, which are incremental changes in velocity, in the strapdown body coordinate system are converted in a coordinate transformation computer from that system into corresponding signals in the stabilized navigation coordinate system.
After transformation into the navigation coordinate system, the incremental velocity signals are integrated or summed to form updated velocity signals. The rotation sensor and accelerometer signals are sampled, and the sampled signals are delivered to a computer which is programmed to accept the signals and to calculate both velocities along the three axes in the stabilized navigation coordinate system and attitude angles relative to this system.
A rotation matrix is created in the attitude integration apparatus to transform vector body-coordinate signals (for example, incremental velocity component signals) from the body coordinate system of the instruments to the navigation coordinate system. The transformed signals are used to calculate and create signals that are measures of the local geographical position of the aircraft and the direction of the local gravity. The transformation matrix also yields signals that are measures of the angular orientation of the supporting vehicle relative to the navigation coordinate system.
The data used to compute the transformation matrix is sampled at finite periodic intervals, causing the bandwidth of the signals to be limited. When the instruments sense vibrations that occur at frequencies above or near the upper limit of the bandwidth of the transformation, where the response is poor, rectification errors occur in the calculated incremental velocity signals, and the navigation coordinate system signals are degraded. The rectification errors producing such degrading are called sculling errors.
A sculling error for a first strapped down axis is caused by a periodic angular displacement about a second axis perpendicular to that axis, multiplied by the periodic acceleration along a third axis perpendicular to the first and second axes.
To reduce the sculling error in strapdown systems, the sampling rate of the instrument signals can be increased. The upper limit of the sampling rate is set by the capabilities of the computer. An increase in sampling rate in a fast computer would likely increase the number of its calculations. The faster the computer, the greater its initial cost. The larger number of calculations might also require a prohibitively sophisticated computer with large power demand.
Instead of increasing the iteration rate for the transformation of incremental velocity from one coordinate system to the other, one might use a sculling compensation algorithm which has the effect of reducing sculling errors while only moderately increasing the computational requirements.
One could use both a faster sampling and sculling compensation to improve further the transformation of incremental velocity from body coordinates to navigation coordinates.